Method of selecting receive antennas for MIMO systems

ABSTRACT

A method of performing receive antenna selection is presented. The method executes a determination operation for a set of receive antennas, determines a maximum result of the determination operation for two of the antennas, eliminates one of the two antennas from the set of antennas, and repeats the determination and elimination process until only a predetermined number of antennas remain in the set. The signals from these remaining antennas are then processed. The present invention reduces receiver complexity and cost.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of prior U.S. application Ser. No.11/897,312, filed Aug. 30, 2007, which is a continuation of prior U.S.application Ser. No. 11/321, 785, filed Dec. 29, 2005, now U.S. Pat. No.7,283,798, which is a continuation of prior U.S. application Ser. No.10/324,168, filed Dec. 19, 2002, now U.S. Pat. No. 7,006,810, each ofwhich are incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

Not applicable.

FIELD OF THE INVENTION

The present invention relates generally to systems having a plurality ofreceive antennas and, more particularly, to selecting a number ofreceive antennas from the plurality of receive antennas and processingsignals from the selected antennas.

BACKGROUND OF THE INVENTION

Multiple Input Multiple Output (MIMO) systems are known to those ofordinary skill in the art. In a MIMO system, a stream of bits isdemultiplexed into a predetermined number of substreams. Each substreamis sent out over a different antenna. The signals get mixed through thewireless channel. Signal processing is applied to the signals at the setof receive antennas to unscramble the data. The unscrambled data streamsare multiplexed into the original high rate bit stream. In such systems,only a portion (e.g. if three substreams were used, only one third) ofthe spectrum which would normally have been required is actually used.

Orthogonal Frequency Division Multiplexing (OFDM) is known to those ofordinary skill in the art. OFDM is a modulation technique useful fortransmitting large amounts of data over a radio wave. The OFDM techniquemodulates multiple carriers at different frequencies with the samesymbol rate such that the signals can be recovered without mutualinterference. The receiver acquires the signal, digitizes the acquiredsignal, and performs a Fast Fourier Transform (FFT) on the digitizedsignal to get back to the frequency domain. The modulation is thenrecovered on each carrier. This technique results in a large amount ofdata being transmitted in a relatively small bandwidth.

The MIMO systems provide high spectral efficiency. Multiple transmitmultiple receive antenna links increase the capacity of MIMO and MIMOOFDM systems. However, the implementation of high spectral efficiency isdifficult due to the complexity of the systems and the resultant highcosts.

It would, therefore, be desirable to provide a method of selectingreceive antennas for MIMO and MIMO OFDM systems which reduces the costand complexity of the MIMO and MIMO OFDM receivers.

SUMMARY OF THE INVENTION

In accordance with the present invention, a method of performing receiveantenna selection is presented. The method executes a determinationoperation for a set of receive antennas, determines a maximum result ofthe determination operation for two of the antennas, eliminates one ofthe two antennas from the set of antennas, and repeats the determinationand elimination process until only a predetermined number of antennasremain in the set. The signals from these remaining antennas are thenprocessed.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of this invention, as well as the inventionitself, may be more fully understood from the following description ofthe drawings in which:

FIG. 1 is a block diagram of a portion of a MIMO/MIMO OFDM system;

FIG. 2 is a flow chart of the present method;

FIG. 3 is a graph of outage probability in a MIMO OFDM with an SNR of 10db;

FIG. 4 is a graph of outage probability in a MIMO OFDM with an SNR of 30db; and

FIG. 5 is a graph of frame error rate (FER) in a MIMO OFDM.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIG. 1, a prior art MIMO/MIMO OFDM system is shown. In theMIMO/MIMO OFDM system, a stream of bits 6 is demultiplexed bydemultiplexer/transmitter 1 into a predetermined number of substreams.Each substream is sent out over a different transmit antenna 2 a-2 f bydemultiplexer transmitter 1. The signals transmitted by the transmitantennas 2 a-2 f get mixed while traveling through the wireless channel5. The signals are received by receive antennas 3 a-3 f. The receivedsignals are coupled from the receive antennas 3 a-3 f toreceiver/multiplexer 4. Signal processing is applied to the signals atthe set of receive antennas to unscramble the data. The unscrambled datastreams are then demultiplexed into a high rate bit stream 7, which is acopy of the high rate bit stream 6.

As described above, MIMO and MIMO OFDM systems require relativelycomplex and expensive receivers. A method is presented by whichperforming receive antenna selection is provided, thereby reducing thecomplexity and cost of the receiver in MIMO and MIMO OFDM systems.

It is known that the incremental gain of additional receive antennas inMIMO and MIMO ODFM systems is negligible when the number of receiveantennas K is larger than the number of transmit antennas M. Hence,through receive antenna selection the reduced receiver complexity ispossible without significant loss in the capacity of the system. Thereare several selection methods based on the capacity or thesignal-to-interference and noise power ratio (SINR). These approachesrequire

$\quad\begin{pmatrix}K \\S\end{pmatrix}$computations of their own criteria, i.e., the capacity or the SINR,where K is the number of receive antennas and S represents the number ofselected antennas.

A MIMO system with K receive antennas and M transmit antennas will beused to describe the present invention. In slowly time-varying flatfading channel (also known as a Rayleigh fading channel) the receivedvector can be modeled as:y=x+w=Hs+w  Equation (1)where y is the received vector with size K×1, x is the data component ofy, K by M matrix H represents the channel, M×1 vector s is thetransmitted vector with an identity correlation matrix and w is thenoise vector.

Each element in channel matrix H is an independent complex Gaussianrandom variable with a variance equal to unity. The transmitted vector sis normalized such that Tr{ss^(H)}=P where s^(H) is the hermitiantranspose of vector s, and P is the total transmitted power. The entriesof w are independent and identically distributed, and are defined byw(i)˜N(O, σ²) where N indicates normal distribution and aσ² is the noisepower). The entries are independent over time and i.

S receive antennas are selected out of K antennas according to severalcriteria. By checking the capacity, S receive antennas are chosen out ofK antennas in a way that the capacity is maximized. Alternatively, byexamining the SINR, which is directly related to bit or symbol errorrate, the selection of S receive antennas out of K antennas can also beperformed.

In one embodiment, the receiver selects S antennas that allow amaximization of the capacity

$\begin{matrix}{C_{s} = {\underset{S{(\overset{\sim}{H})}}{\max\;\log_{2}}{{I_{s} + {\frac{\rho}{M}\overset{\sim}{H}{\overset{\sim}{H}}^{H}}}}}} & {{Equation}\mspace{14mu}(2)}\end{matrix}$where I_(s) is the S×S identity matrix,

$\rho = \frac{P}{\sigma^{2}}$is the mean signal-to-noise ratio (SNR) per receiver branch, reducedmatrix {tilde over (H)} is created by deleting K−S rows of channelmatrix H, and S({tilde over (H)}) represents the set of all possiblereduced matrices {tilde over (H)}.

Since there are

$\quad\begin{pmatrix}K \\S\end{pmatrix}$possible reduced channel matrices {tilde over (H)}, the capacity isevaluated as many times as

$\begin{pmatrix}K \\S\end{pmatrix}.$

The determinant in Equation (2) can be written as

$\begin{matrix}{{{I_{s} + {\frac{\rho}{M}\overset{\sim}{H}{\overset{\sim}{H}}^{H}}}} = {\prod\limits_{k = 1}^{r}\left( {1 + {\frac{\rho}{M}{\lambda_{k}}^{2}}} \right)}} & {{Equation}\mspace{14mu}(3)}\end{matrix}$where r is the rank of the reduced channel matrix {tilde over (H)} andλ_(k) is the singular value of reduced channel matrix {tilde over (H)}.The rank and the singular values are maximized for the maximum capacity.

There may be a case in which there are two rows of the channel matrix Hwhich are identical. Clearly only one of these rows should be selectedin reduced channel matrix {tilde over (H)}. Since these two rows carrythe same information, either row of these two rows can be deletedwithout losing any information about the transmitted vector. In additionif the rows have different powers (i.e. magnitude square of the norm ofthe row), then the lower power row can be deleted.

When there are no identical rows then the next two rows whosecorrelation is the next highest are chosen for the deletion. In thismanner the reduced channel matrix {tilde over (H)} whose rows aremaximally uncorrelated and have maximum powers are obtained. This leadsto several methods for determining the highest correlation rate amongthe set of receive antennas.

A first method (method 1) for determining the highest correlation rateis performed in accordance with the formula:

$\begin{matrix}{{{Corr}\left( {k,l} \right)} = {\left\langle {\frac{h_{k}}{{h_{k}}^{2}},h_{l}} \right\rangle }} & {{Equation}\mspace{14mu}(4)}\end{matrix}$

where X={1, 2, . . . K}, h_(k) is the kth row of channel matrix H, h_(l)is the lth row of channel matrix H, k≠l, and k, lεX.

The correlation rate is determined by taking the absolute value of theinner product of the two arguments. The result is the square root of thesum of the products of each value in the h vectors.

A second method (method 2) for determining the highest correlation rateis performed in accordance with the formula:

$\begin{matrix}{{{Corr}\left( {k,l} \right)} = {\left\langle {\frac{h_{k}}{h_{k}},h_{l}} \right\rangle }} & {{Equation}\mspace{14mu}(5)}\end{matrix}$

where X={1, 2, . . . K}, h_(k) is the kth row of channel matrix H, h_(l)is the lth row of channel matrix H, k≠l, and k, lεX.

Another method (method 3) for determining the highest correlation rateis performed in accordance with the formula:

$\begin{matrix}{{{Corr}\left( {k,l} \right)} = {\left\langle {\frac{h_{k}}{h_{k}},\frac{h_{l}}{h_{l}}} \right\rangle }} & {{Equation}\mspace{14mu}(6)}\end{matrix}$

where X={1, 2, . . . K}, h_(k) is the kth row of channel matrix H, h_(l)is the lth row of channel matrix H, k>l, and k, lεX.

Yet another method (method 4) for determining the highest correlationrate is performed in accordance with the formula:Corr(k·l)=|

h _(k) ,h _(l)

|  Equation (7)

where X={1, 2, . . . K}, h_(k) is the kth row of channel matrix H, h_(l)is the lth row of channel matrix H, k>l, and k, lεX.

Method 4 is the least complex method to implement. The above methods donot require the SNR value and are based mainly on the correlationE{y_(k)y_(l) ⁺} where E is the expected value of the inner product oftwo output vector y's average, of the sum of the products of each valuein y's.

As an alternative method when the SNR is available, the mutualinformation between received vector Y_(k) and received vector Y_(l) isused. The zero-valued mutual information means the received vector Y_(k)and the received vector Y_(l) carry totally different information. Thisoccurs when the corresponding channel vector h_(k) and h_(l) areorthogonal. The channel vector h_(k) is defined as the k-th row of thechannel matrix H. If the mutual information is maximum, the receivedvector y_(k) and the received vector y_(l) carry the same information sothat one of them can be deleted. The mutual information is defined asI(y _(k) ;y _(l))=H(y _(k))+H(y _(l))−H(y _(k) ,y _(l))  Equation (8)

In the MIMO system the mutual information can be written as

$\begin{matrix}{{I\left( {y_{k};y_{l}} \right)} = {\log\frac{\left( {{{h_{k}}^{2}\frac{\rho}{M}} + 1} \right)\left( {{{h_{l}}^{2}\frac{\rho}{M}} + 1} \right)}{{\left( {{{h_{k}}^{2}\frac{\rho}{M}} + 1} \right)\left( {{{h_{l}}^{2}\frac{\rho}{M}} + 1} \right)} - {{\left\langle {h_{k},h_{l}} \right\rangle }^{2}\frac{\rho^{2}}{M^{2}}}}}} & {{Equation}\mspace{14mu}(9)}\end{matrix}$Since the mutual information is bounded as following0≦I(y _(k) ;y _(l))≦min(H(y _(k)),H(y _(l)))  Equation (10)the normalized mutual information is defined below as

$\begin{matrix}{{I_{0}\left( {y_{k};y_{l}} \right)} = \frac{I\left( {y_{k};y_{l}} \right)}{\min\left( {{H\left( y_{k} \right)},{H\left( y_{l} \right)}} \right)}} & {{Equation}\mspace{14mu}(11)}\end{matrix}$as a measure of how close the two random variables are. The entropycalculation of the received vector y_(k) requires both the signal andnoise power, whereas the mutual information needs the SNR only.

This can be overcome as follows. The scaling of receive vector y_(k) toc·y_(k), where the non-zero real number c is chosen in the way that thenoise variance is equal to one, will not normalize mutual information.The scaling does not change the mutual information while the entropy ofc·y_(k) becomes

$\begin{matrix}\begin{matrix}{{H\left( {c - y_{k}} \right)} = {\log\left( {{c^{2}{h_{k}}^{2}\frac{P}{M}} + {c^{2}\sigma^{2}}} \right)}} \\{= {\log\left( {{{h_{k}}^{2}\frac{\rho}{M}} + 1} \right)}}\end{matrix} & {{Equation}\mspace{14mu}(12)}\end{matrix}$The normalized mutual information is redefined as

$\begin{matrix}{{I_{0}\left( {y_{k};y_{l}} \right)} = \frac{I\left( {{c \cdot y_{k}};{c \cdot y_{l}}} \right)}{\min\left( {{H\left( {c \cdot y_{k}} \right)},{H\left( {c \cdot y_{l}} \right)}} \right)}} & {{Equation}\mspace{14mu}(13)}\end{matrix}$Then, the normalized mutual information becomes

$\begin{matrix}{{I_{0}\left( {y_{k};y_{l}} \right)} = \frac{I\left( {y_{k};y_{l}} \right)}{\min\left( {{\log\left( {{{h_{k}}^{2}\frac{\rho}{M}} + 1} \right)},{\log\left( {{{h_{l}}^{2}\frac{\rho}{M}} + 1} \right)}} \right)}} & {{Equation}\mspace{14mu}(14)}\end{matrix}$

The procedure for calculating the normalized mutual information (method5) is done in accordance with the formula:I ₀(y _(k) ;y _(l))  Equation (15)

where X={1, 2, . . . K}, k>l, and k, lεX.

The mutual information based technique can also be applied to the datacomponent x_(k) in order to avoid requiring the SNR value. Then, themutual information between the data component x_(k) and the datacomponent x_(l) is

$\begin{matrix}{{I\left( {x_{k};x_{l}} \right)} = {\log{\frac{{h_{k}}^{2}{h_{l}}^{2}}{{{h_{k}}{h_{l}}^{2}} - {\left\langle {h_{k},h_{l}} \right\rangle }^{2}}.}}} & {{Equation}\mspace{14mu}(16)}\end{matrix}$Similarly, the normalized mutual information is defined below as

$\begin{matrix}\begin{matrix}{{I_{0}\left( {x_{k};x_{l}} \right)} = \frac{I\left( {{c \cdot x_{k}};{c \cdot x_{l}}} \right)}{\min\left( {{H\left( {c \cdot x_{k}} \right)},{H\left( {c \cdot x_{l}} \right)}} \right)}} \\{= \frac{I\left( {x_{k};x_{l}} \right)}{\min\left( {{\log{h_{k}}^{2}},{\log{h_{l}}^{2}}} \right)}}\end{matrix} & {{Equation}\mspace{14mu}(17)}\end{matrix}$The procedure for calculating the normalized mutual information (method6) is done in accordance with the formula:I ₀(x _(k) ;x _(l))  Equation (18)

where X={1, 2, . . . K}, k>l, and k, lεX.

Having described receiver antenna selection techniques with respect toMEMO systems, the following describes receiver selection techniques withrespect to MIMO OFDM systems.

In a MIMO OFDM system with N subcarriers, the channel matrix under timeinvariant channel can be modeled as a block diagonal matrix

$\begin{matrix}{{{H = {\begin{bmatrix}{H(1)} & 0 & \cdots & 0 \\0 & {H(2)} & 0 & \vdots \\\vdots & 0 & \ddots & 0 \\0 & \cdots & 0 & {H(N)}\end{bmatrix}\mspace{14mu}{where}}}{{H(n)} = \begin{bmatrix}H_{11{(n)}} & H_{12{(n)}} & \cdots & {H_{1\; M}(n)} \\{H_{21}(n)} & {H_{22}(n)} & \cdots & {H_{2\; M}(n)} \\\vdots & \vdots & \ddots & \vdots \\{H_{K\; 1}(n)} & {H_{K\; 2}(n)} & \cdots & {H_{KM}(n)}\end{bmatrix}}}\mspace{11mu}} & {{Equation}\mspace{14mu}(19)}\end{matrix}$represents the channel matrix between K receive and M transmit antennasat subcarrier n. The capacity becomes

$\begin{matrix}{C = {\sum\limits_{n = 1}^{N}\;{\log_{2}{{{I_{K} + {\frac{\rho}{M}{H(n)}{H^{H}(n)}}}}.}}}} & {{Equation}\mspace{14mu}(20)}\end{matrix}$

In the correlation based methods (methods 1-4 described above for a MIMOsystem) the correlation must now be averaged over the subcarriers toprovide the same function for a MIMO OFDM system. For example, thecorrelation formula used in method 1 for a MIMO system is modified toaccount for the subcarriers to become method 7 which is performed inaccordance with the formula:

$\begin{matrix}{{{Corr}\left( {k,l} \right)} = {{\sum\limits_{n = 1}^{N}\left\langle {\frac{h_{k}(n)}{{{h_{k}(n)}}^{2}},{h_{l}(n)}} \right\rangle}}} & {{Equation}\mspace{14mu}(21)}\end{matrix}$

where X={1, 2, . . . K}, h_(k)(n) is the kth row of channel matrix atsubcarrier n H(n), k≠l, and k, lεX.

Similarly, the correlation formula used in method 2 for a MIMO system ismodified to become method 8 for a MIMO OFDM system, which is performedin accordance with the formula:

$\begin{matrix}{{{Corr}\left( {k,l} \right)} = {{\sum\limits_{n = 1}^{N}\left\langle {\frac{h_{k}(n)}{{h_{k}(n)}},{h_{l}(n)}} \right\rangle}}} & {{Equation}\mspace{14mu}(22)}\end{matrix}$

where X={1, 2, . . . K}, h_(k)(n) is the kth row of channel matrix atsubcarrier n H(n), k≠l, and k, lεX.

The correlation formula used in method 3 for a MIM system is replacedwith method 9 for a MIMO OFDM system, which is performed in accordancewith the formula:

$\begin{matrix}{{{Corr}\left( {k,l} \right)} = {{\sum\limits_{n = 1}^{N}\left\langle {\frac{h_{k}(n)}{{h_{k}(n)}},\frac{h_{l}(n)}{{h_{l}(n)}}} \right\rangle}}} & {{Equation}\mspace{14mu}(23)}\end{matrix}$

where X={1, 2, . . . K}, h_(k)(n) is the kth row of channel matrix atsubcarrier n H(n), k≠l, and k, lεX.

The correlation formula used in method 4 for a MIMO system is replacedwith method 10 for a MIMO OFDM system, which is performed in accordancewith the formula:

$\begin{matrix}{{{Corr}\left( {k,l} \right)} = {{\sum\limits_{n = 1}^{N}\left\langle {{h_{k}(n)},{h_{l}(n)}} \right\rangle}}} & {{Equation}\mspace{14mu}(24)}\end{matrix}$

where X={1, 2, . . . K}, h_(k)(n) is the kth row of channel matrix atsubcarrier n H(n), k≠l, and k, lεX.

Defining the received vector at the k-th receive antenna asy_(k)=[y_(k)(1) y_(k)(2) . . . y_(k)(N)]^(T) where y_(k)(n) is the k-threceive antenna output at the n-th subcarrier, the mutual information inthe MIMO OFDM system becomesI(y _(k) ;y _(l))=H(y _(l))−H(y _(k) ,y _(l))  Equation (25)The block diagonal property of the MIMO OFDM channel matrix defines themutual information to be

$\begin{matrix}{{I\left( {y_{k};y_{l}} \right)} = {{\sum\limits_{n = 1}^{N}{H\left( {y_{k}(n)} \right)}} + {H\left( {y_{l}(n)} \right)} - {H\left( {{y_{k}(n)},{y_{l}(n)}} \right)}}} & {{Equation}\mspace{14mu}(26)}\end{matrix}$Hence, the mutual information-based techniques used in the MIMO systemsare modified to use the following normalized mutual information and totake into account the subcarrier n. Method 5 for a MIMO system isreplaced by method 11 for a MIMO OFDM system wherein:

$\begin{matrix}{{I_{0}\left( {y_{k};y_{l}} \right)} = \frac{\sum\limits_{n}{I\left( {{y_{k}(n)};{y_{l}(n)}} \right)}}{\min\left( {{\sum\limits_{n}{H\left( {c \cdot {y_{k}(n)}} \right)}},{\sum\limits_{n}{H\left( {{c \cdot y_{l}}(n)} \right)}}} \right)}} & {{Equation}\mspace{14mu} 27}\end{matrix}$where y_(k) is the k-th receive vector at subcarrier n, y_(l) is thel-th receive vector at subcarrier n, c is a constant, H is a channelmatrix, k>l, and k, lεX.

Similarly, method 6 for a MIMO system is replaced by method 12 for aMIMO OFDM system which is performed in accordance with the formula:

$\begin{matrix}{{I_{0}\left( {x_{k};x_{l}} \right)} = \frac{\sum\limits_{n}{I\left( {{x_{k}(n)};{x_{l}(n)}} \right)}}{\min\left( {{\sum\limits_{n}{H\left( {c \cdot {x_{k}(n)}} \right)}},{\sum\limits_{n}{H\left( {c \cdot {x_{l}(n)}} \right)}}} \right)}} & {{Equation}\mspace{14mu} 28}\end{matrix}$

where y_(k) is the k-th receive vector at subcarrier n, y_(l) is thel-th receive vector at subcarrier n, c is a constant, H is a channelmatrix, k>l, and k, lεX.

Referring now to FIG. 2, a flow chart of the presently disclosed methodis depicted. The rectangular elements are herein denoted “processingblocks” and represent computer software instructions or groups ofinstructions. The diamond shaped elements, are herein denoted “decisionblocks,” represent computer software instructions, or groups ofinstructions which affect the execution of the computer softwareinstructions represented by the processing blocks.

Alternatively, the processing and decision blocks represent stepsperformed by functionally equivalent circuits such as a digital signalprocessor circuit or an application specific integrated circuit (ASIC).The flow diagrams do not depict the syntax of any particular programminglanguage. Rather, the flow diagrams illustrate the functionalinformation one of ordinary skill in the art requires to fabricatecircuits or to generate computer software to perform the processingrequired in accordance with the present invention. It should be notedthat many routine program elements, such as initialization of loops andvariables and the use of temporary variables are not shown. It will beappreciated by those of ordinary skill in the art that unless otherwiseindicated herein, the particular sequence of steps described isillustrative only and can be varied without departing from the spirit ofthe invention. Thus, unless otherwise stated the steps described beloware unordered meaning that, when possible, the steps can be performed inany convenient or desirable order.

The process starts at step 10 wherein a set of receive antennas of aMIMO or MIMO OFDM receiver are identified. In the present example, theset of receive antennas comprise six antennas referred to as antenna1-antenna 6 respectively. While a set of six receive antennas are usedin this example, it should be appreciated that any number of receiveantennas could be used.

The process then proceeds to step 20 where a determination is made as tothe number of antennas to be used. For example, if the MIMO or MIMO OFDMreceiver has a set of six receive antennas, it may be desirable to onlyprocess signals from two of the six antennas. While only two of sixreceive antennas are used in this example, it should be appreciated thatany number of receive antennas could be used.

At step 30 an operation is executed for each antenna of the set ofreceive antennas. The operation may relate to determining the amount ofcorrelation between each antenna which each other antenna of the set, ordetermining an amount of mutual information between antennas of the set.

At step 40 the two antennas which yielded the maximum results of theoperation performed in step 30 are selected. In the present example, ifa correlation operation was performed and it turned out that antennas 4and 6 were the most closely correlated pair, than these two antennas areselected.

Following step 40, step 50 is executed wherein one of the two antennas(antenna 4, antenna 6) is deleted from the set of receive antennas.Therefore, either antenna 4 or antenna 6 is deleted from the set ofreceive antennas. Thus, initially the set of receive antennas includedantennas 1-6, and antenna 4 is deleted, leaving five remaining antennasin the set of receive antennas (antennas 1-3 and 5-6).

At step 60 a determination is made as to whether the remaining set ofantennas has the desired number of antennas left in the set. In thisinstance five antennas are remaining, while it is desired to have onlytwo remaining, so steps 40 and 50 are executed again. Each iteration ofsteps 40 and 50 result in another antenna being removed from the set ofreceive antennas. Steps 40 and 50 are repeated until there are only twoantennas remaining in the set of receive antennas. Once the desirednumber of antennas is left in the set of receive antennas, step 70 isexecuted.

At step 70, the antennas remaining in the set of receive antennas areused, and signals from these antennas are processed. The method thenends at step 80.

Referring now to FIGS. 3 and 4, the outage probability of each disclosedmethod in a MIMO OFDM system under frequency selective Rayleigh fadingchannel is shown. The number of subcarriers is 64. The maximum delayspread (T_(d)) is ¼ of the symbol duration and the r.m.s. delay spread(τ_(d)) is assumed to be ¼ of the maximum delay spread with anexponential power distribution. The number of transmit and receiveantennas is 2 and 6, respectively. FIG. 3 uses an SNR of 10 db, whileFIG. 4 uses a SNR value of 30 db. Each method selects 2 out of 6 receiveantennas. For FIG. 3, the best selection is shown by line 210, and theworst selection is shown by line 220. The selection using methods 7-12are shown by lines 230, 240, 250, 260, 270 and 280 respectively. ForFIG. 4, the best selection is shown by line 310, and the worst selectionis shown by line 320. The selection using methods 7-12 are shown bylines 330, 340, 350, 360, 370 and 380 respectively. Among fast methodsthe mutual information based methods (methods 11 and 12) outperform thecorrelation-based methods (methods 7-10).

The FER (frame error rate) is shown in FIG. 5 when the bandwidthefficiency is 10 bits/sec/Hz. The worst selection has 3 dB loss at 10e⁻³ FER. Method 11 (line 470) has less than 0.5 dB loss while thecorrelation based methods (methods 7-10, designated by lines 430, 440,450 and 460 respectively) exhibit from 1 to 1.5 dB loss. The performanceof the fast method 12 (line 480) is comparable to or even better thanthat of the method 11 (line 470) at high FER while at low FER the method12 (line 480) has similar performance with the correlation based methods(not shown). Method 12 (line 480) has good performance overall while itdoes not require the SNR value as in the correlation based methods.

A method of performing receive antenna selection for MIMO and MIMO OFDMsystems has been described. The method executes a determinationoperation for a set of receive antennas, determines a maximum result ofthe determination operation for two of the antennas, eliminates one ofthe two antennas from the set of antennas, and repeats the determinationand elimination process until only a predetermined number of antennasremain in the set. The signals from these remaining antennas are thenprocessed. The present invention reduces receiver complexity and cost.

Having described preferred embodiments of the invention it will nowbecome apparent to those of ordinary skill in the art that otherembodiments incorporating these concepts may be used. Additionally, thesoftware included as part of the invention may be embodied in a computerprogram product that includes a computer useable medium. For example,such a computer usable medium can include a readable memory device, suchas a hard drive device, a CD-ROM, a DVD-ROM, or a computer diskette,having computer readable program code segments stored thereon. Thecomputer readable medium can also include a communications link, eitheroptical, wired, or wireless, having program code segments carriedthereon as digital or analog signals. Accordingly, it is submitted thatthat the invention should not be limited to the described embodimentsbut rather should be limited only by the spirit and scope of theappended claims.

What is claimed is:
 1. A method for selecting a desired number ofreceive antennas from a set of receive antennas, the method comprising:determining, by a processor, a signal-to-interference and noise powerratio of the set of receive antennas; determining, by the processor, aplurality of correlations between different rows of a channel matrixassociated with the set of receive antennas, wherein each row of thechannel matrix corresponds to a receive antenna of the set of receiveantennas and wherein the determining the plurality of correlationscomprises determining an absolute value of an inner product of thedifferent rows of the channel matrix; identifying, by the processor, apair of receive antennas having a greatest correlation of the pluralityof correlations from the set of receive antennas based on thesignal-to-interference and noise power ratio; eliminating, by theprocessor, one receive antenna of the pair of receive antennas havingthe greatest correlation, wherein the eliminating one receive antenna ofthe pair of receive antennas is based on a capacity of the set ofreceive antennas and the signal-to-interference and noise power ratio ofthe set of receive antennas; and repeating the identifying a pair ofreceive antennas and the eliminating one receive antenna of the pair ofreceive antennas in response to determining that a number of receiveantennas remaining in the set of receive antennas is greater than thedesired number of receive antennas.
 2. The method of claim 1, whereineliminating one receive antenna of the pair of receive antennascomprises determining a receive antenna having a smallest power from thepair of receive antennas and eliminating the receive antenna having thesmallest power.
 3. The method of claim 1, wherein the identifying a pairof receive antennas having a greatest correlation comprises determininga pair of receive antennas having a greatest amount of mutualinformation.
 4. The method of claim 1, wherein eliminating one receiveantenna of the pair of receive antennas comprises determining a receiveantenna having a smaller entropy from the pair of receive antennas andeliminating the receive antenna having the smaller entropy.
 5. Themethod of claim 1, wherein identifying a pair of receive antennas havinga greatest correlation comprises determining a correlation for amultiple input multiple output orthogonal frequency divisionmultiplexing system.
 6. The method of claim 1, wherein identifying apair of receive antennas having a greatest correlation comprisesdetermining an amount of mutual information in a multiple input multipleoutput orthogonal frequency division multiplexing system.
 7. The methodof claim 1, wherein identifying the pair of receive antennas having agreatest correlation from the set of receive antennas is based on theformula${{Corr}\left( {k,l} \right)} = {\left\langle {\frac{h_{k}}{{h_{k}}^{2}},h_{l}} \right\rangle }$wherein the different rows of the channel matrix comprise h_(k), ak^(th) row of the channel matrix, and h_(l), an l^(th) row of thechannel matrix, such that k≠l, and k, lεX, where X={1, 2 . . . K}. 8.The method of claim 1, wherein identifying the pair of receive antennashaving a greatest correlation from the set of receive antennas is basedon the formula${{Corr}\left( {k,l} \right)} = {\left\langle {\frac{h_{k}}{h_{k}},h_{l}} \right\rangle }$wherein the different rows of the channel matrix comprise h_(k), ak^(th) row of the channel matrix, and h_(l), an l^(th) row of thechannel matrix, such that k≠l, and k, lεX, where X={1, 2 . . . K}. 9.The method of claim 1, wherein identifying the pair of receive antennashaving a greatest correlation from the set of receive antennas is basedon the formula${{Corr}\left( {k,l} \right)} = {\left\langle {\frac{h_{k}}{h_{k}},\frac{h_{l}}{h_{l}}} \right\rangle }$wherein the different rows of the channel matrix comprise h_(k), ak^(th) row of the channel matrix, and h_(l), an l^(th) row of thechannel matrix, such that k>l, and k, lεX, where X={1, 2 . . . K}. 10.The method of claim 1, wherein identifying the pair of receive antennashaving a greatest correlation from the set of receive antennas is basedon the formulaCorr(k·l)=|<h _(k) ,h _(l)>| wherein the different rows of the channelmatrix comprise h_(k), a k^(th) row of the channel matrix, and h_(l), anl^(th) row of the channel matrix, such that k>l, and k, lεX, where X={1,2 . . . K}.
 11. A non-transitory computer readable medium storingcomputer program instructions for selecting a desired number of receiveantennas from a set of receive antennas, which, when executed on aprocessor, cause the processor to perform operations comprising:determining a signal-to-interference and noise power ratio of the set ofreceive antennas; determining a plurality of correlations betweendifferent rows of a channel matrix associated with the set of receiveantennas, wherein each row of the channel matrix corresponds to areceive antenna of the set of receive antennas and wherein thedetermining the plurality of correlations comprises determining anabsolute value of an inner product of the different rows of the channelmatrix; identifying a pair of receive antennas having a greatestcorrelation of the plurality of correlations from the set of receiveantennas based on the signal-to-interference and noise power ratio;eliminating one receive antenna of the pair of receive antennas havingthe greatest correlation, wherein the eliminating of the one receiveantenna of the pair of receive antennas is based on a capacity of theset of receive antennas and the signal-to-interference and noise powerratio of the set of receive antennas; and repeating the identifying apair of receive antennas and the eliminating of the one receive antennaof the pair of receive antennas in response to determining that a numberof receive antennas remaining in the set of receive antennas is greaterthan the desired number of receive antennas.
 12. The non-transitorycomputer readable medium of claim 11, wherein the eliminating of the onereceive antenna of the pair of receive antennas further comprisesdetermining a receive antenna having a smallest power from the pair ofreceive antennas and eliminating the receive antenna having the smallestpower.
 13. The non-transitory computer readable medium of claim 11,wherein the identifying of the pair of receive antennas having agreatest correlation further comprises determining a pair of receiveantennas having a greatest amount of mutual information.
 14. Thenon-transitory computer readable medium of claim 11, wherein theeliminating of the one receive antenna of the pair of receive antennasfurther comprises determining a receive antenna having a smaller entropyfrom the pair of receive antennas and eliminating the receive antennahaving the smaller entropy.
 15. The non-transitory computer readablemedium of claim 11, wherein the identifying of the pair of receiveantennas having a greatest correlation further comprises determining acorrelation for a multiple input multiple output orthogonal frequencydivision multiplexing system.
 16. The non-transitory computer readablemedium of claim 11, wherein the identifying of the pair of receiveantennas having a greatest correlation further comprises determining anamount of mutual information in a multiple input multiple outputorthogonal frequency division multiplexing system.
 17. Thenon-transitory computer readable medium of claim 11, wherein theidentifying of the pair of receive antennas having a greatestcorrelation from the set of receive antennas is based on the formula${{Corr}\left( {k,l} \right)} = {\left\langle {\frac{h_{k}}{{h_{k}}^{2}},h_{l}} \right\rangle }$wherein the different rows of the channel matrix comprise h_(k), ak^(th) row of the channel matrix, and h_(l), an l^(th) row of thechannel matrix, such that k≠l, and k, lεX, where X={1, 2 . . . K}. 18.The non-transitory computer readable medium of claim 11, wherein theidentifying of the pair of receive antennas having a greatestcorrelation from the set of receive antennas is based on the formula${{Corr}\left( {k,l} \right)} = {\left\langle {\frac{h_{k}}{h_{k}},h_{l}} \right\rangle }$wherein the different rows of the channel matrix comprise h_(k), ak^(th) row of the channel matrix, and h_(l), an l^(th) row of thechannel matrix, such that k≠l, and k, lεX, where X={1, 2 . . . K}. 19.The non-transitory computer readable medium of claim 11, wherein theidentifying of the pair of receive antennas having a greatestcorrelation from the set of receive antennas is based on the formula${{Corr}\left( {k,l} \right)} = {\left\langle {\frac{h_{k}}{h_{k}},\frac{h_{l}}{h_{l}}} \right\rangle }$wherein the different rows of the channel matrix comprise h_(k), ak^(th) row of the channel matrix, and h_(l), an l^(th) row of thechannel matrix, such that k>l, and k, lεX, where X={1, 2 . . . K}. 20.The non-transitory computer readable medium of claim 11, wherein theidentifying of the pair of receive antennas having a greatestcorrelation from the set of receive antennas is based on the formulaCorr(k·l)=|<h _(k) ,h _(l)>| wherein the different rows of the channelmatrix comprise h_(k), a k^(th) row of the channel matrix, and h_(l), anl^(th) row of the channel matrix, such that k>l, and k, lεX, where X={1,2 . . . K}.